Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answers
The statements that are true about the quadratic function and its graph include the following:
The value of f(–10) = 82The graph of the function is a parabola.The graph contains the point (20, –8).How to determine the true statements about this function and its graph?In Mathematics, the graph of any quadratic function or equation always forms a parabola because it is a u-shaped curve. For the given quadratic function, the graph is a upward parabola because the coefficient of x² is positive i.e when the value of "a" is greater than zero.
Next, we would determine the statements about the quadratic function and its graph that are true:
At point (-10, 82), we have:
f(x) = 1/5 x² – 5x + 12
f(x) = x²/5 – 5x + 12
f(-10) = -10²/5 – 5(-10) + 12
f(-10) = 82
At point (20, -8), we have:
f(x) = 1/5 x² – 5x + 12
f(x) = x²/5 – 5x + 12
f(20) = 20²/5 – 5(20) + 12
f(20) = -8
In conclusion, the graph of this quadratic function does not contain the point (0, 0) as shown in the image attached below.
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Complete Question:
Consider the quadratic function f(x) = 1/5 x² – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Related Questions
scores on an iq test are normally distributed. the test is designed so that the mean is 100 and standard deviation is 15. (a) what percentage of the population has an iq above 120?
Answers
From the normal distribution it is calculated that 9.18% of people has an iq over 120.
Normal distributions are crucial to statistics because they are widely used in the natural and social sciences to represent real-valued regressors with unknown distributions.
Some of their significance can be attributed to the central limit theory. This claim states that, in some cases, the average of many samples (observations) of a stochastic process with limited mean and variance constitutes itself as a random variable, whose distribution merges to a normal distribution as the number of samples increases.Because of this, the distributions of physical values, such as error margins, which are expected to be the sum of many independent events, are frequently near to normal.We have to find P( X > 120 )
Thus find z score for x =120
[tex]z=\frac{x-\mu}{\sigma}=\frac{120-100}{15}=\frac{20}{15}=1.33[/tex]
Thus we get:
P(X>120) = P(Z>1.33)
P(X>120) = 1 - P(Z<1.33)
P( Z < 2.67) = 0.9082
Thus
P(X>140) = 1 - P(Z<2.67)
P(X>140) = 1 - 0.9082
P(X>140) = 0.0918
Percentage = 9.18%
Therefore 9.18% of people has an iq over 120.
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Write an
equation of the line passing through point P(-1,-4) that is parallel to
y = -6x + 8.
Answers
y = -6x -25 is equation of slope intercept .
What exactly does slope intercept mean?
A method of expressing a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line is drawn the y-axis is known as the y-intercept, and the slope refers to how steep the line is.The equation is y = -6x + 8
compare with equation y=mx+b
slope m = -6
Use the point-slope method
y = -6x + 8
point P(-1,-4) point given (x1,y1)
y-y1=m(x-x1) point-slope form
y - ( -1 ) = -6 ( x - (-4))
y + 1 = -6 ( x + 4 )
y + 1 = -6x - 24
y = -6x -25
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what are the steps of simplifying the fraction 1244/2000 to its lowest term?
Answers
Explanation: Find the GCD (or HCF) of numerator and denominator
GCD of 1244 and 2000 is 4
Divide both the numerator and denominator by the GCD:
1244 ÷ 4
2000 ÷ 4
Reduced fraction:
311/500
Therefore, 1244/2000 simplified to lowest terms is 311/500.
A pile of sand has a weight of 65 kg.
Some of the sand is put into a small sack.
The rest of the sand is put into a large sack.
The sand in the large sack weighs 15 kg more than the sand in the small sack.
What is the weight of the sand in the small sack?
Answers
Answer:
25kg
Step-by-step explanation:
65=x+x+15
65-15=2x
50=2x
25=x
this graph shows the height of a tree over a 5 year growing peroid calculate the rate of change of height per year
Need explanation on how to solve ASAP
Answers
Answer: It jupes by 2 each year the rate is 2 to 1 year
Step-by-step explanation:
In zero years it alretey 1m so we can go to 1 where its 3 it juped by two more
can you help with these two questions please
Answers
So let’s start with that
Area of circle is 3.14(r^2)
We are given the diameter as 20m
So radius is 10m
Thus area = 3.14(100)= 314 sq metres
Now each box covers 58 sq metre
So no of boxes = 314/58= 5.41
Rounding to 1 significant figure
It’s 5 boxes
Clearly we are underestimating it as it’s around 5 boxes and a half
For the second question just equate their area
(11)(10)/2 = 22b
=> b= 2.5cm
The quadratic equation [tex]( k - 1 )x^{2} + 2x + ( 2k - 3 ) = 0[/tex] , where k is R, has real distinct roots.
Find the range of possible values for k.
Answers
The possible values of k such that the quadratic equation has real distinct roots are 1 / 2 and 2.
What are the possible values of k associated to quadratic equation?
In this problem we find the case of a quadratic equation, of which the values of a variable k must be found such that the polynomial have real distinct roots. This can be done by using the discriminant of the quadratic formula, which is defined below:
For a · x² + b · x + c = 0, the discriminant is:
b² - 4 · a · c > 0
Then, if we know that a = k - 1, b = 2 and c = 2 · k - 3, then the possible values of k are:
2² - 4 · (k - 1) · (2 · k - 3) > 0
4 - (4 · k - 4) · (2 · k - 3) > 0
4 - (8 · k² - 8 · k - 12 · k + 12) > 0
8 · k² - 20 · k + 8 > 0
Whose form form is shown below:
8 · (k² - (20 / 8) · k + 1) = 0
8 · (k² - (5 / 2) · k + 1) = 0
8 · (k - 2) · (k - 1 / 2) = 0
The possible values of k are 1 / 2 and 2.
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Write an equation in point-slope form of the line that passes through the given point and with the given slope m. A. (1, -8) m= -9
Answers
The point-slope form of a line is:
y = mx + b
where m is the slope and b is the y-intercept
Replacing with point (1, -8) and m= -9, we get:
-8 = (-9)(1) + b
-8 = -9 + b
-8 + 9 = b
1 = b
Then, the equation is:
y = -9x + 1
Complete the two-way frequency table below, which shows the relationship between students who enroll in advanced algebra and physics in a particular high school. From a sample of 40 students, it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both. How many students are enrolled in either algebra or physics?
Awnsers:
33
38
2
5
Answers
1. The frequency table will be:
Physics - Not in algebra = 9
Not in physics (Algebra) = 24
Not in physics (Not in algebra) = 2
Total (Not in physics) = 26
Total = 11
2. The students are enrolled in either algebra or physics is B. 38.
How to calculate the value?It was found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both.
Not in physics for algebra = 24
Not in physics = 2
The Total for the value will be:
= 24 + 2= 26
The students enrolled in either will be:
= Algebra + Physics - Both
= 29 + 14 - 5
= 43 - 5
= 38
This illustrates the concept of addition and subtraction of numbers.
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Answer:
Its B. 38
Step-by-step explanation:
Hope this helps :)
Find x of the triangle
Answers
Answer: The answer is 20°
Step-by-step explanation:
I think it’s 20° but I’m only in the 6th grade and I got my 180 ruler for this into the screen
Please help! Please and thank you
Answers
Answer:
8 divided by 2
Step-by-step explanation:
Simplify 5^3 times 5^4
a: 5^12
b: 5^7
c: 5^9
d: 25^7
Answers
Answer:
b
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then
[tex]5^{3}[/tex] × [tex]5^{4}[/tex]
=[tex]5^{(3+4)}[/tex]
= [tex]5^{7}[/tex]
Describe the translation from AB to A’B’
Answers
The translation from AB to A’B’ is (x, y) → (x + 9, y + 2).
What is Translation in Math?The translation is a type of transformation in mathematics. When a shape is transformed, the original shape is referred to as the preimage, and the translated shape is referred to as the image.In mathematics, a translation is the movement of a shape to the left or right and/or up or down. The translated shapes appear to have the same size as the original shape, and hence the shapes are congruent. They were simply relocated in one or more directions.Given:
The coordinates of A(preimage) are (-5,1).
The coordinates of A'(image) are (4,3).
From the coordinates of the translated image, A'B' we can determine the transformations.
The translation applied to the point (-5,1) are (x, y) → (x + 9, y + 2).
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How many positive integer pairs (x,y) satisfy 4x+12y=640?
Answers
The number of positive pairs that satisfy the given linear function is given by: 161.
When a function is positive and when it is negative?We have to look at the graph of the function relative to the x-axis, more specifically if the function is above or below the x-axis, as follows:
A function is positive when it is above the x-axis.A function is negative when it is below the x-axis.In the context of this problem, the function is defined as follows:
4x + 12y = 640.
Which is a linear function, as both x and y have exponents of 1. The ordered pairs on the function are the values above the line. With integer numbers, that is, numbers that have no decimal parts, from the graph of the function given at the end of the answer, the values of x for which the function is positive is given by:
0 ≤ x ≤ 160.
Containing 161 values of x. Since this represents a function, each of the 161 values of x is associated to a value of y, meaning that there are 161 positive integer pairs (x,y) that satisfy the equation 4x + 12y = 640.
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I need the right answer so please be correct
Answers
Answer: 8
Step-by-step explanation:
found slope
URGENTTTY PLS PLS HELP !! GRAPH TOO PLS !!
Answers
3. Toby randomly interviewed 70 patrons at a country music concert to determine their favorite type of music. Based on the results of his survey, he made the following claim:
Two out of three concert-goers prefer country music.
Which of the following statements best describes why this is not a valid claim?
O Only people on the floor level were surveyed.
Not enough patrons at the concert were surveyed.
The concert-goers were not randomly surveyed.
Toby only surveyed patrons at a country music concert who are probably biased toward country music.
Al changes se
Answers
Answer: Two out of three concert-goers prefer country music.
Step-by-step explanation:
Toby is interviewing country music concert participants, and therefore isn't getting a diverse spread of interviewees and isn't getting accurate data.
Mrs. Scott rented a jeep. The rental charge is a flat fee of
$115 plus $12.50 per hour. Her bill is $152.50, not
including tax. Write and solve an equation that could be
used to find the number of hours she rented the jeep
Answers
Step by step
Using y intercept form
y = mx + b
Flat fee of $115 is y intercept or “b”
The $12.50 per hour is the rate or “m”
$152.50 is the total
So your equation is
$152.50 = $12.50x + $115
To solve subtract $115 from both sides to isolate x
$152.50 - $115 = $12.50x + $115 -$115
$152.50 = $12.50x
Divide both sides by $12.50 to solve for x
x = 12.2 hours
An electrician leans an extension ladder against the outside wall of a
house so that it reaches an electric box 28 feet up. The ladder makes an
angle of 71° with the ground. Find the length of the ladder. Round your
answer to the nearest hundredth of a foot if necessary.
Answers
Answer:
30 feet
Step-by-step explanation:
i used a ruler, mm side. 1 mm = 1 foot
draw a horizontal line.
draw a vertical line 28mm high
use a protractor to find a line that connects to the base and top of vertical line.
measure said line
Answer:
Step-by-step explanation:
\text{sin }\color{purple}{71}=\frac{\color{green}{\text{opposite}}}{\color{#EB0000}{\text{hypotenuse}}}=\frac{\color{green}{28}}{\color{#EB0000}{x}}
sin 71=
hypotenuse
opposite
=
x
28
\text{sin }71=
sin 71=
\,\,\frac{28}{x}
x
28
\frac{\text{sin }71}{1}=
1
sin 71
=
\,\,\frac{28}{x}
x
28
x\text{ sin }71=
x sin 71=
\,\,28
28
Cross multiply.
\frac{x\text{ sin }71}{\text{ sin }71}=
sin 71
x sin 71
=
\,\,\frac{28}{\text{ sin }71}
sin 71
28
Divide both sides by sin 71
x=\frac{28}{\text{ sin }71}=29.613379...\approx29.61
x=
sin 71
28
=29.613379...≈29.61
44+400 divided by (4+62)-24
Answers
Answer:
10.57
Step-by-step explanation:
44+400=444
(4+62)-24=
66-24=42
444/42=10.57
I NEED HELP!!!
50 POINTS!!!
Answers
slope is 3;
rise/run = y/x
6/2 = 3/1
<
Find the time-and-a-half pay rate by multiplying the hourly wage, $22 by
by 1-1/2
When the hourly wage is $22, the time-and-a-half pay rate is $
(Simplify your answer.)
Answers
consequently, the time and a half rate will be 33 dollars per hour according to the query.
What is the logic behind time and a half pay rate and how tocalculate it?A higher rate of pay known as "time and a half" is normally only applied to hours that are over 40 in a workweek or that are worked extra.
Companies have different overtime pay practices, with time and a half as a typical rate.
Simply said, it means that for each hour performed within the time and a half window, the employee will receive payment in addition to their regular hourly rate of one half of that amount.
Time and a Half Rate = Hourly Rate * 1.5
According to the given question:
Time and a half rate =22$*1-1/2
=22$*1.5
=33$ per hour
Therefore, According to the question given the Time and a pay half rate will
be 33$ per hour.
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Help Please!!
Unit 4 lesson 11 geometry Parallel and Perpendicular Lines Unit Test
I have been doing well in this test till this question... any help is appreciated!!
Answers
The values of x = 14 and y = 12
In the diagram given, there are two parallel lines and three angles formed by cutting the parallel lines.
So here, angles (2x+7)° and (3x-7)° are corresponding angles.
That is they occupy relatively same position, that is both are above each parallel line.
So they are equal angles.
i.e., 2x+7 = 3x-7
⇒ 3x-2x = 7 +7
⇒ x = 14
Now the angles 2x+7° and 12y+1° are supplementary angles.
Supplementary angles are formed on a straight line between a line cutting the straight line.
That is their sum = 180°
i.e., 2x+7° + 12y+1° = 180
⇒ 2 x 14 + 7 + 12y +1 = 180
⇒ 28 + 8 +12y = 180
⇒ 36 +12y = 180
⇒ 12y = 180 -36
⇒ 12y = 144
⇒ y = 12
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What is the value of −5 + (−14) + 53?
Answers
Answer:
34
Step-by-step explanation:
The value would be 34
what does it mean translate the figure 5 units up
Answers
By definition. a Translation is a transformation in which a figure is moved a fixed distance in a fixed direction.
The Image is the figure obtained after the transformation and the Pre-Image is the original figure.
In this case, you know that the figure shown in the picture must be translated 5 units up. Therefore, the rule for this transformation is:
[tex](x,y)\rightarrow(x,y+5)[/tex]You can identify that the marked point on the Pre-Image has the following coordinates:
[tex]\mleft(-4,-3\mright)[/tex]Therefore, applying the rule for this transformation, you get that the coordinates of the marked point in the final figure, are:
[tex]\mleft(-4,-3\mright)\rightarrow\mleft(-4,-3+5\mright)\rightarrow(-4,2)[/tex]The answer is:
Coordinates of the marked point in the original figure:
[tex](-4,-3)[/tex]Coordinates of the marked point in the final figure:
[tex]\mleft(-4,2\mright)[/tex]Help me please!! due at 8pm tonight 10/12/22
Answers
Answer:
y=3x+3
Step-by-step explanation:
Use rise/run
Answer:
y=-9x+5
Step-by-step explanation:
If the water level rises 12 centimeters every 7 minutes and you record the data point of (21,y), what is the value of y? Use slope to justify your answer. please help deadlines at 1200 am sunday
Answers
The value of y-coordinate from the given information is 36.
Given that, the water level rises 12 centimeters every 7 minutes and you record the data point of (21, y).
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
According to the question the water rises 12 cm every 7 minutes. Taking x to represent the time in minutes and y to represent the rise in cm then, find the rise y in time x as;
7 minutes = 12 cm
1 minute
(1×12)/7 = 12/7
Hence in 1 minute, the rise is 12/7 cm
Thus in 11 minutes, the rise will be ;
21 × 12/7 = 3 × 12 = 36 cm
So, (x, y) will be (21, 36)
Therefore, the value of y-coordinate from the given information is 36.
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A woman bought some large frames for $10 each and some small frames for $5 each at a closeout sale. If she bought 23 frames for $160, find how many of each type she bought
Answers
A woman purchased 12 little frames and 10 large frames.
We create an algebraic equation in this question.
Algebraic equation: what is it?An algebraic equation is a mathematical statement that makes two expressions equal to one another.
In most circumstances, an algebraic equation consists of a variable, coefficients, and constants.
According to question, the equation will be
Let x = large frame
y = small frame
x + y = 22 ---(1)
10x + 5y = 160 ---(2)
Now, solve the eq(1) and eq(2),
we get, x = 10
and, y = 12
If you want to cross-check you can do like that,
large frame price = $10
and, x = 10 (means 10 large frames women bought)
so the price will be = $ 10 * 10
= $100
Now, for the small frame price = $5
and, y = 12 (means 10 large frames women bought)
so the price will be = 12 * $5
= $60
Now total price is given = $160
and if we add both the prices of large and small frames = $100 + $60
we get, same as total price = $160
Therefore, we can say that woman bought 10 large frames and 12 small frames.
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Helpppppppppppppppppppppppp
Answers
the actual amount is 78000 dollar
Step-by-step explanation:
one pack cigarettes cost 25 dollar
3 pack cigarettes costs 75 dollar
20 years × 52 =1040
1040 weeks
1040 × 75 dollar
78000 dollar
Help me with this i need to submit this assignment tyy
i think its ez but yk.. im lazy
Answers
Answer:
3x3x3x3=81
.......................